Question: Vanessa is 27 years older than Michael. Vanessa and Michael first met 3 years ago. Nineteen years ago, Vanessa was 4 times older than Michael. How old is Vanessa now?
We can use the given information to write down two equations that describe the ages of Vanessa and Michael. Let Vanessa's current age be $v$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $v = m + 27$ Nineteen years ago, Vanessa was $v - 19$ years old, and Michael was $m - 19$ years old. The information in the second sentence can be expressed in the following equation: $v - 19 = 4(m - 19)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $v$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = v - 27$ . Substituting this into our second equation, we get the equation: $v - 19 = 4($ $(v - 27)$ $ -$ $ 19)$ which combines the information about $v$ from both of our original equations. Simplifying the right side of this equation, we get: $v - 19 = 4v - 184$ Solving for $v$ , we get: $3 v = 165$ $v = 55$.